NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4.

- Squares and Square Roots Class 8 Ex 6.1
- Squares and Square Roots Class 8 Ex 6.2
- Squares and Square Roots Class 8 Ex 6.3

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 6 |

Chapter Name |
Squares and Square Roots |

Exercise |
Ex 6.4 |

Number of Questions Solved |
9 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4

**Ex 6.4 Class 8 Maths Question 1.**

Find the square root of each of the following numbers by Division method :

**(i)** 2304

**(ii)** 4489

**(iii)** 3481

**(iv)** 529

**(v)** 3249

**(vi)** 1369

**(vii)** 5776

**(viii)** 7921

**(ix)** 576

**(x)** 1024

**(xi)** 3136

**(xii)** 900

**Solution:**

**Ex 6.4 Class 8 Maths Question 2.**

Find the number of digits in the square root of each of the following numbers (without any calculation) :

**(i)** 64

**(ii)** 144

**(iii)** 4489

**(iv)** 27225

**(v)** 390625

**Solution:**

**Ex 6.4 Class 8 Maths Question 3.**

Find the square root of the following decimal numbers :

**(i)** 2.56

**(ii)** 7.29

**(iii)** 51.84

**(iv)** 42.25

**(v)** 31.36

**Solution:**

**(i)** Here, the number of decimal places is already even. So, mark off periods and proceed as under :

∴ \(\sqrt { 2.56 } =1.6\)

**(ii)** Here, the number of decimal places are already even. So, mark off periods and proceed as under :

∴ \(\sqrt { 7.29 } =2.7\)

**(iii)** Here, the number of decimal places are already even. So, mark off periods and proceed as under :

∴ \(\sqrt { 51.84 } =7.2\)

**(iv)** Here, the number of decimal places are already even. So, mark off periods and proceed as under :

∴ \(\sqrt { 42.25 } =6.5\)

**(v)** Here, the number of decimal places are already even. So, mark off periods and proceed as under :

∴ \(\sqrt { 31.36 } =5.6\)

**Ex 6.4 Class 8 Maths Question 4.**

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

**(i)** 402

**(ii)** 1989

**(iii)** 3250

**(iv)** 825

**(v)** 4000

**Solution:**

**(i)** Let us try to find the square root of 402.

This shows the (20)^{2} is less than 402 by 2. So, in order to get a perfect square, 2 must be subtracted from the given number.

∴ Required perfect square number = 402 – 2 = 400

Also, \(\sqrt { 400 } =20\)

**(ii)** Let us try to find the square root of 1989.

This shows that (44)^{2} is less than 1989 by 53. So, in order to get a perfect square, 53 must be subtracted from the given number.

∴ Required perfect square number = 1989 – 53 = 1936

Also, \(\sqrt { 1936 } =44\)

**(iii)** Let us try to find the square root of 3250.

This shows that (57)^{2} is less than 3250 by 1. So, in order to get a perfect square, 1 must be subtracted from the given number.

∴ Required perfect number = 3250 -1 = 3249

Also, \(\sqrt { 3249 } =57\)

**(iv)** Let us try to find the square root of 825.

This shows that (28)^{2} is less than 825 by 41. So, in order to get a perfect square, 41 must be subtracted from the given number.

∴ Required perfect square number = 825 – 41 = 784

Also, \(\sqrt { 784 } =28\)

**(v)** Let us try to find the square root of 4000.

This shows that (63)^{2} is less than 4000 by 31. So, in order to get a perfect square, 31 must be subtracted from the given number.

∴ Required perfect square number = 4000 – 31 = 3969

Also, \(\sqrt { 3969 } =63\)

**Ex 6.4 Class 8 Maths Question 5.**

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

**(i)** 525

**(ii)** 1750

**(iii)** 252

**(iv)** 1825

**(v)** 6412

**Solution:**

**(i)** We try to find out the square root of 525.

**(ii)** We try to find out the square root of 1750.

**(iii)** We try to find out the square root of 252.

**(iv)** We try to find out the square root of 1825.

**(v)** We try to find out the square root of 6412.

**Ex 6.4 Class 8 Maths Question 6.**

Find the length of the side of a square whose area is 441 m^{2}.

**Solution:**

**Ex 6.4 Class 8 Maths Question 7.**

In a right triangle ABC, ∠B = 90°.

**(a)** If AB = 6 cm, BC = 8 cm, find AC.

**(b)** If AC = 13 cm, BC = 5 cm, find AB.

**Solution:**

**Ex 6.4 Class 8 Maths Question 8.**

A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

**Solution:**

Let us find the square root of 1000.

This shows that (31)^{2} is less than 1000 by 39 and (32)^{2} =1024. Thus, the gardener needs 1024 -1000 = 24 plants more to plant in such a way that the number of rows and the number of columns remain the same.

**Ex 6.4 Class 8 Maths Question 9.**

There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

**Solution:**

Let us find the square root of 500.

This shows that (22)^{2} = 484 is less than 500 by 16.

∴ 16 students have to go out for others to do the P.T. practice as per condition.

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